This study was intended to accomplish two objectives, to improve upon the mobile bed
modelling law on beach profile response and to extend the modelling law to three dimensional
applications, specifically to inlet model studies. Four existing scaling laws on beach profile response
under storm wave conditions were examined based on two dimensional wave tank tests. The tests
consisted of three different geometrical scales simulating a target prototype profile evolution test
selected from the German large wave flume (GWK) experiments. Since the intent was to extend the
modelling law for offshore application, the performance of modeling laws was evaluated beyond the
nearshore profile. The beach profile was divided into two regions, the nearshore dune region and the
offshore bar-profile region. Separate evaluation criteria were developed and applied to the test results.
Based on the comparisons, a new modelling law was proposed.

Experiments were then carried out in three-dimensional wave basin to examine the proposed
modelling law and the results were reasonably successful but were rather limited.

Vellinga's relationships or Wang, et.al.'s guidance. The geometrical relationships of
these two set of criteria are very similar but the time scale is different. Vellinga's
approach is largely empirical based on dimensional analysis of physical quantities.
Wang (1990) took a slightly different approach by the inspection of the basic govern-
ing equation to deal with a restricted case, here the two dimensional beach profile
changes under the influence of wave action. Since their approach is based on the
actual sediment transport equation it offers the major advantage that the modeling
laws can be rationally modified to accommodate different hypotheses. These model-
ing laws, in turn, can be used to explain the physical process that is being modelled,
not simply producing match scales between model and prototype. Therefore, the
approach by Wang et.al is adopted here with a brief derivation of their results then
followed by a proposed variation.

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The basic equation, which balancing the spatial change of sediment transport rate

and the temporal change of beach profile, is the two-dimensional sediment conserva-

tion equation:

O =Oq (3.15)
at 9x
where h is the bottom elevation, q is the volumetric sediment transport rate in

the direction x. Non-dimensionalize the equation:

h qt (3.16)
at 8A Ox

where the overbar refers to non-dimensional quantities and q,, t,, 6, A represent

the reference values of sediment transport rate, the morphorogical time scale, vertical

and horizontal geometrical scale respectively.

To maintain similitude between the model and prototype requires

N t = 1 (3.17)
NsN

where N refers to the ratio of prototype to model.

It is assumed that suspended load transport mode predominates the sediment

transport inside the surf zone which is approximated by the following equation,

q, = hVc (3.18)

where h is depth, V is mean transport velocity and c is mean sediment concentration.

The suspended sediemnt concentration is then assumed to be directly proportional

to the ratio of stirring power due to turbulence and the settling power due to gravity

and can be expressed as (Hattori and Karvamata, 1980):

pu' u'
c Poc (3.19)
(ps p)W SW

24
where u' is the turbulent intensity, W is the particle settling velocity and S is the

submerged specific weight.

The ratio of turbulent velocity and wave induced velocity is a function of surf

zone parameter as suggested by Thorton (1978), i.e.,

U
S= f(() (3.20)

The surf zone parameter is defined as TanP/3/Hb/Lo with Tan/ the beach slope,

Hb the breaking wave height, and Lo the deep water wave length.

Physically, this equation states that if the surf zone property is similar, the turbu-

lent intensity should be proportional to the mean velocity scale provided the surf zone

parameter is preserved. Since in a wave field u is proportional to H/T, combining

Eqs. (1.17), (1.18) and (1.19) with Eq. (1.16) gives the following scaling law,

NvNf()NtNH = 1 (3.21)
NANwNTNs
where the subscripts correspond to various physical quantities given earlier. It should

be noted here Nv is the scale ratio of the mean transport velocity which must not be